Application of High Dimensional B-Spline Interpolation in Solving the Gyro-Kinetic Vlasov Equation Based on Semi-Lagrangian Method (Communications in Computational Physics, 2017)
The computation efficiency of high dimensional (3D and 4D) B-spline interpolation,constructed by classical tensor product method, is improved greatly byprecomputing the B-spline function. This is due to the character of NLT code, i.e. onlythe linearised characteristics are needed so that the unperturbed orbit as well as valuesof the B-spline function at interpolation points can be precomputed at the beginning ofthe simulation. By integrating this fixed point interpolation algorithm into NLT code,the high dimensional gyro-kinetic Vlasov equation can be solved directly without operatorsplitting method which is applied in conventional semi-Lagrangian codes. Inthe Rosenbluth-Hinton test, NLT runs a few times faster for Vlasov solver part andconverges at about one order larger time step than conventional splitting code.